Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Exponents

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #3 : Simplifying Exponents

Simplify:

$\frac{x^{6}zy^{-9}}{x^{-4}z^2y^3}$

Possible Answers:

$\frac{x^{10}z^3}{y^6}$

$x^2z^{-1}y^6$

$\frac{y^6}{x^{10}z^3}$

$\frac{x}{yz^2}$

$\frac{x^{10}}{zy^{12}}$

Correct answer:

$\frac{x^{10}}{zy^{12}}$

Explanation:

Step 1: Use the division of exponents rule. Subtract the exponents in the numerator from the exponents in the denominator.

${x^{6+4}z^{1-2}y^{-9-3}$

$x^{10}z^{-1}y^{-12}$

Step 2: Represent the negative exponents as positive ones by moving them to the denominator:

${\color{Red} \frac{x^{10}}{zy^{12}}}$

Report an Error

Example Question #4705 : Algebra 1

Simplify this expression:

$\frac{x^{2}y^{-3}z^{4}}{x^{3}y^{-2}z^{2}}$

Possible Answers:

$\frac{yz^{2}}{x}$

$xyz^{2}$

$\frac{1}{xyz^{2}}$

$\frac{z^{2}}{xy}$

$\frac{xy}{z^{2}}$

Correct answer:

$\frac{z^{2}}{xy}$

Explanation:

When different powers of the same variable are multiplied, the exponents are added. When different powers of the same variable are divided, the exponents are subtracted. So, as an example:

$\frac{x^{3}}{x} = x^{\left ( 3-1\right )} = x^{2}$

For the above problem,

$\frac{x^{2}}{x^{3}} = \frac{1}{x} ; \frac{y^{-3}}{y^{-2}} = \frac{y^{2}}{y^{3}} = \frac{1}{y} ; \frac{z^{4}}{z^{2}} = z^{2}$

Therefore, the expression simplifies to:

$\left ( \frac{1}{x} \right ) \left ( \frac{1}{y} \right ) z^{2} = \frac{z^{2}}{xy}$

Report an Error

Example Question #4706 : Algebra 1

Simplify the rational expression.

$\frac{12x^2y^4z^6}{6xz^{12}}$

Possible Answers:

$\frac{x}{2z^6}$

$\frac{2xy^4}{z^2}$

$\frac{x}{2z^2}$

$\frac{2xy^4}{z^6}$

Correct answer:

$\frac{2xy^4}{z^6}$

Explanation:

$\frac{12x^2y^4z^6}{6xz^{12}}$

To simplify variables with exponents through division, you must subtract the exponent in the denominator from the numerator.

$\frac{12}{6}(x^{2-1})(y^{4-0})(z^{6-12})=2xy^4z^{-6}=\frac{2xy^4}{z^6}$

Remember that negative exponents will eventually be moved back to the denominator.

Report an Error

Example Question #11 : Multiplying And Dividing Exponents

Simplify:

$\frac{9ab^2c}{4c^3} \times \frac{a^2b^2}{3a^3c}$

Possible Answers:

$\frac{3a^6b^4}{4c^3}$

$\frac{3a^3b^4}{4c^4}$

$\frac{3b^4}{4ac^2}$

$\frac{3b^4}{4c^3}$

Correct answer:

$\frac{3b^4}{4c^3}$

Explanation:

In this problem, you have two fractions being multiplied. You can first divide and cancel the coefficients in the numerators and denominators, by dividing 9 and 3 each by 3:

$\frac{9ab^2c}{4c^3} \times \frac{a^2b^2}{3a^3c} = \frac{3ab^2c}{4c^3} \times \frac{a^2b^2}{a^3c}$

Next you can multiply the two numerators, and multiply the two denominators. Remember that when multiplying like variables with exponents, you add the exponents together:

$\frac{3ab^2c}{4c^3} \times \frac{a^2b^2}{a^3c} = \frac{3a^3b^4c}{4a^3c^4}$

If a variable shows up in both the numerator and denominator, you can simplify by subtracting the numerator's exponent by the denominator's exponent. If you end up with a negative exponent in the numerator, you can move the variable and exponent to the denominator to make it positive:

$\frac{3b^4}{4c^3}$

Report an Error

Example Question #12 : Multiplying And Dividing Exponents

Simplify the following:

$\frac{10x^2y^3z}{7xz^3} \times \frac{21xyz^2}{5y}$

Possible Answers:

$\frac{6xy^2}{z}$

6x^2y^3

6x^2y^3z

$\frac{6x}{y^2z}$

Correct answer:

6x^2y^3

Explanation:

In this problem, you have two fractions being multiplied. You can first divide and cancel the coefficients in the numerators and denominators, by dividing 10 and 5 each by 5 and dividing 21 and 7 each by 7:

$\frac{10x^2y^3z}{7xz^3} \times \frac{21xyz^2}{5y} = \frac{2x^2y^3z}{xz^3} \times \frac{3xyz^2}{y}$

Next you can multiply the two numerators, and multiply the two denominators. Remember that when multiplying like variables with exponents, you add the exponents together:

$\frac{2x^2y^3z}{xz^3} \times \frac{3xyz^2}{y} = \frac{6x^3y^4z^3}{xyz^3}$

If a variable shows up in both the numerator and denominator, you can simplify by subtracting the numerator's exponent by the denominator's exponent:

$\frac{6x^3y^4z^3}{xyz^3} = 6x^2y^3$

Report an Error

Example Question #341 : Exponents

Simplify $\frac{a^{4}b^{2}}{6a^{3}b}\div \frac{2b^{5}}{12a^{7}}$

Possible Answers:

$\frac{a^8}{b^4}$

$\frac{2a^8}{b^4}$

$\frac{b^6}{36a^6}$

$\frac{b^4}{a^8}$

Correct answer:

$\frac{a^8}{b^4}$

Explanation:

Rewrite so that you are multiplying the reciprocal of the second fraction:

$\frac{a^{4}b^{2}}{6a^{3}b}\times \frac{12a^{7}}{2b^{5}}$

You can then simplify using rules of exponents:

$\frac{12a^{11}b^2}{12a^3b^6}=\frac{a^8}{b^4}$

Report an Error

Example Question #342 : Exponents

Simplify the following:

$\frac{2a^3bc}{3a^2bc^4} \times \frac{15ab^3c^2}{5a^3b^5c^2}$

Possible Answers:

2ab^2c^3

$\frac{2c^3}{ab^2}$

$\frac{2ab}{c^3}$

$\frac{2}{ab^2c^3}$

Correct answer:

$\frac{2}{ab^2c^3}$

Explanation:

In this problem, you have two fractions being multiplied. You can first divide and cancel the coefficients in the numerators and denominators. The two coefficients in the denominators multiply up to 15, allowing you to divide and cancel those two coefficients with the 15 in the numerator:

$\frac{2a^3bc}{3a^2bc^4} \times \frac{15ab^3c^2}{5a^3b^5c^2} = \frac{2a^3bc}{a^2bc^4} \times \frac{ab^3c^2}{a^3b^5c^2}$

Next you can multiply the two numerators, and multiply the two denominators. Remember that when multiplying like variables with exponents, you add the exponents together:

$\frac{2a^3bc}{a^2bc^4} \times \frac{ab^3c^2}{a^3b^5c^2} = \frac{2a^4b^4c^3}{a^5b^6c^6}$

$\frac{2a^4b^4c^3}{a^5b^6c^6} = \frac{2}{ab^2c^3}$

Report an Error

Example Question #343 : Exponents

Simplify $x^3\cdot x^{-2}\cdot x^4$ .

Possible Answers:

$x^{-12}$

$x^{-24}$

$\frac{1}{x^{24}}$

$\frac{1}{x^5}$

x^5

Correct answer:

x^5

Explanation:

When multiplying variables with the same base, you add the exponents. So, $x^{3+(-2)+4}=x^{1+4}=x^5$ .

Report an Error

Example Question #4333 : Algebra 1

Simplify the expression.

y^2z^3y^4z^5y^6

Possible Answers:

$y^{10}z^8$

$y^{15}z^3$

$y^{12}z^{10}$

$y^9z^{11}$

$y^{12}z^8$

Correct answer:

$y^{12}z^8$

Explanation:

y^2z^3y^4z^5y^6

Rearrange the expression so that the $\small y$ and $\small z$ variables of different powers are right next to each other.

y^2y^4y^6z^3z^5

When multiplying the same variable with different exponents, it is the same as adding the exponents: $a^ba^c=a^{b+c}$ . Taking advantage of this rule, the problem can be rewritten.

$y^{2+4+6}z^{3+5}$

$y^{6+6}z^8$

$y^{12}z^8$

Report an Error

Example Question #4775 : Algebra 1

Simplify:

$\frac{30a^{2}b}{c}*\frac{bc^{2}}{5c}$

Possible Answers:

$\frac{6a^{2}b^{2}}{c^{4}}$

$6a^{2}b^{2}$

$6ab^{2}$

$6a^{2}b^{2}c^{4}$

$\frac{6a^{2}b^{2}c^{2}}{c^{2}}$

Correct answer:

$6a^{2}b^{2}$

Explanation:

Combine like terms in the numerator and the denominator. Use the rules of exponents to combine and in the numerator and and in the denominator. Remember that $x^{a}*x^{b}=x^{a+b}$ Then, divide 30 by 5 (the GCF).

$\frac{30a^{2}b*b*c^{2}}{5c*c}=\frac{30a^{2}b^{2}c^{2}}{5c^{2}}=\frac{6a^{2}b^{2}c^{2}}{c^{2}}$

The GCF rule can also be used to remove $c^{2}$ from the numerator and the deonominator. $c^{2}$ goes into $c^{2}$ once.

$\frac{6a^{2}b^{2}c^{2}}{c^{2}}=6a^{2}b^{2}$

Report an Error

View Algebra 2 Tutors

Caroline
Certified Tutor

University of Florida, Bachelor of Science, Psychology.

View Algebra 2 Tutors

Joshua
Certified Tutor

The Ohio State University, Bachelor of Science, Mathematics.

View Algebra 2 Tutors

Sean
Certified Tutor

University of Chicago, Bachelor in Arts, Philosophy. University of Chicago, Master of Public Policy, Public Policy Analysis.

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

French Tutors in Washington DC, Algebra Tutors in Philadelphia, Statistics Tutors in San Francisco-Bay Area, Algebra Tutors in San Francisco-Bay Area, Math Tutors in Phoenix, LSAT Tutors in Seattle, Math Tutors in Chicago, ISEE Tutors in San Francisco-Bay Area, MCAT Tutors in San Diego, Computer Science Tutors in Washington DC

Popular Courses & Classes

GRE Courses & Classes in Los Angeles, GMAT Courses & Classes in Atlanta, LSAT Courses & Classes in Phoenix, LSAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Philadelphia, MCAT Courses & Classes in Miami, SSAT Courses & Classes in Boston, ACT Courses & Classes in Atlanta, Spanish Courses & Classes in Miami, Spanish Courses & Classes in San Diego

Popular Test Prep

GMAT Test Prep in Denver, SSAT Test Prep in Boston, GRE Test Prep in Los Angeles, SSAT Test Prep in Miami, SSAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Houston, GMAT Test Prep in Miami, MCAT Test Prep in Philadelphia, ISEE Test Prep in Dallas Fort Worth, MCAT Test Prep in Houston

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Algebra II : Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #3 : Simplifying Exponents

Example Question #4705 : Algebra 1

Example Question #4706 : Algebra 1

Example Question #11 : Multiplying And Dividing Exponents

Example Question #12 : Multiplying And Dividing Exponents

Example Question #341 : Exponents

Example Question #342 : Exponents

Example Question #343 : Exponents

Example Question #4333 : Algebra 1

Example Question #4775 : Algebra 1

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: